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Jasper Slingsby
No one ever does them…
…but they could save so much pain and suffering if they did!!!
Statistical power is the probability of a hypothesis test finding an effect if there is an effect to be found.
Power analysis is a calculation typically used to estimate the smallest sample size needed for an experiment, given a required significance level, statistical power, and effect size.
Firstly, it helps you plan your analyses before you’ve done your data collection, which is always useful.
Secondly, not knowing the statistical power of your analysis can result in
Type II Error:
Type I Error:
Type I and Type II Errors and how they result in false or missing findings, respectively. Image from Norton and Strube 2001, JOSPT.
Is determined by the combination of the:
We usually use an \(\alpha\) of 0.05 to indicate significant difference.
This is a subjective cut-off, but is generally accepted in the literature…
You have greater statistical power when you have greater differences in means (effect size). P1 vs P3 has greater power than either P1 vs P2 or P2 vs P3.
Greater variability among subjects results in larger standard deviations, reducing our ability to distinguish among groups (i.e. statistical power).
Increasing sample size increases statistical power by improving the estimate of the mean and constricting the distribution of the test statistic (i.e. reducing the standard error).
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